Between DeVos's controversial backing of charter schools without regulation and outspoken support for vouchers and Trump's disdain for the Common Core, the appointment could have far-reaching effects on city schools.

Here's a look at how DeVos and Trump’s ideas for education could affect city schools:

►Trump could siphon $500 million in federal funds away from public schools and put them into educational vouchers

An analysis from the United Federation of Teachers estimated that more than 700,000 students in more than 1,200 city schools could see bigger class sizes, fewer teachers and less enrichment and after-school programs if Trump pulls federal dollars now used for Title 1 funding at public schools with low-income students.

DeVos, a billionaire and Republican donor, played a big role in taking money away from public schools in her home state of Michigan — which has one of the highest number of charter school students in the nation — and is a big donor to Eva Moskowitz's Success Academy Charter Schools.

Trump has been a vocal supporter of school choice — in which parents are either able to choose from alternatives to traditional schools, such as charters, or are given equivalent funds to spend at the school of their choice in the form of vouchers.

“I will establish the national goal of providing school choice to every American child living in poverty,” Trump said in September, adding that he wants to give out $12,000 per student per year from the time they're in kindergarten through their senior year in high school.

That could mean that Trump would divert Federal Title 1 funds that go to public schools serving low-income students to be used instead to help pay for his voucher program, Brooklyn College Professor David Bloomfield said.

If that were to happen, Bloomfield said, “It would be a radical restructuring of American education and threaten the foundations of local school districts.”

DeVos's track record in Michigan was among the reasons she faced more backlash than other education picks, and even other cabinet picks, in general. Pence's involvement to break the tie was the first in history.

But experts said it would take a huge lift to get buy-in from New York, as well as other states, to foot the bill for a voucher program, which could cost states a total of $110 billion out of their own education budgets.

For example, there’s already been a decade-long battle over billions of dollars that New York state owes city schools to provide court-mandated equal funding for the most needy students.

In addition, the voucher system could wreak havoc on school enrollment, which is already strained under the existing system. Parents scramble for a spot in desirable schools while "undesirable" schools remain under-enrolled, he said.

“Most schools that are regarded as successful are oversubscribed, and the paths to expansion include adding more students to them or opening more schools like them, which may be undesirable or take years to occur, respectively,” Pallas wrote.

Vouchers tend to be favored more by special interests and religious schools, Bloomfield said — a group that's currently less represented in the city's educational landscape than public and charter schools.

In New York City, there were nearly 240,000 students in private or parochial schools in the 2014-2015 school year — a fraction of the 1.1 million children in the city's public school system — according to the Independent Budget Office.

By comparison, there were 85,000 students in charter schools in 2014.The most recent breakdown of religious school enrollment available showed that Yeshivas enrolled close to 95,000 students in K-12 in 2012 while Catholic schools enrolled more than 87,000, according to an IBO report. There were 41,000 students in private schools that year.

► Trump might encourage for-profit online schools to expand to K-12

Trump has talked about wanting to encourage more competition in the school system — and called public schools' hold on the nation's educational system a "monopoly."

But his own leadership of the for-profit Trump University — which has spawned three class-action lawsuits across the country, including one in New York — could spur the proliferation of online schools at the pre-K to 12 level, Bloomfield said.

The for-profit online college sector, much like Trump University, has been steadily growing as watchdogs warn that it is rife for abuse.

In an extreme case, an expanded voucher program could incentivize K-12 education to go the way of online universities, with families taking their money to pay for virtual classes, Bloomfield posited.

“A voucher program could shape a fundamental re-organization of education," he said.

►Charters might proliferate — but without proper oversight, many fear.

The charter sector in Michigan is subject to much less regulation than in New York — which is likely why many local charter leaders have been largely silent on DeVos.

Charters in DeVos's home state have questionable records. In Detroit, for instance, about 70 percent of charter schools ranked in the bottom quarter of the state’s schools in the 2013-2014 school year, according to a report from Politico which noted that DeVos led the charge against attempts to regulate the charter industry.

James Merriman, CEO of the New York City Charter School Center, wrote in a Daily News op-ed that there needs to be "meaningful vetting" and that "the growth of at-home, online charter schools is an example of simple greed and inadequate state oversight."

►Trump hates the Common Core — but he may not be the anti-testing parents' champion either.

NYC's growing opt-out movement has seen more and more students sit out the state English and math tests aligned with the Common Core standards in protest of the "excessive testing" culture and the commensurate stress.

While Trump has also made his dislike of the Common Core standards clear, he's not necessarily aligned with the principles of the opt-out movement, either, experts say.

The opt-out philosophy grows out of progressive education, Bloomfield said.

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